# CZ:Mathematics Workgroup

The Citizendium Mathematics Workgroup
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## Core articles

Core articles are those that are as-yet unwritten and so should be prioritised. Please start articles on the topics below. Click here to edit this transcluded list.

## Articles

Click on the [r] after the first definition below to edit this list of transcluded subtopics.

• Mathematics [r]: The study of quantities, structures, their relations, and changes thereof. [e]

## Work plan white paper

The topics below are part of the division of mathematical knowledge to subdisciplines; they come from the 2000 Math. subject classification of the AMS [1] and ZMATH [2], with some minor edits. Each of these top level topics is a big subject, and it is not necessarily our first priority to write a long article on these entries. Our object with outlining this list is to establish a framework. We recommend that when you write a new article, you should try to find a proper node for it. Do not hesitate to put a link for an article you want to work on soon. Feel free to do the same to request a particular important topic to be covered.

Remarks:

• We kept the original MSC numbering in places.
• No, of course its not the whole MSC tree - not even close to it. We should eventually put as much of it as appropriate.
• In some places we really expect some other workgroups (usually the physicists) to do the work alongside - we state where.

Caveats:

• Do not copy articles from Wikipedia without carefully reading them, verifying both scope and focus. Besides, why not consider writing your article from scratch? Often this permits a better logical structure and more coherence. See CZ:How to convert Wikipedia articles to Citizendium articles
• Keep in mind three audiences when writing an article: general readers, math students and professionals.

## Most wanted math entries

From the encyclopedic point of view, the "high priority" articles are probably listed below at the top level of the tree (or in the table of contents). These are, however, relatively wide syntheses. You may want to start with a bit smaller tasks. A collection of important entries to write (of both types) can be found on the Core Articles page (still to be reviewed and reorganized).

Most popular Wikipedia math entries are: Pi, Mathematics , prime number, computer, trapezoid. These come from the list of 1000 most viewed pages in March 2007.[3] This varies heavily over the time.

## The classification

#### 00-XX General

(for calculus see 26-XX Real functions below)

• elementary mathematics (pre-university level)
Elementary functions
trigonometric function
point line plane solid stubs
elementary algebra
for suggestions of useful articles to write see also here (pre-calculus or geometry sections)

Euclid
Euler

#### 12-XX Field theory and polynomials

• 12Dxx Real and complex fields
real numbers
complex numbers

#### 14-XX Algebraic geometry

hyperelliptic curve
Kummer surfaces

#### 20-XX Group theory and generalizations

• 20Axx Foundations
• 20Bxx Permutation groups
• 20Cxx Representation theory of groups [See also 19A22 (for representation rings and Burnside rings)]
• 20Dxx Abstract finite groups
• 20Exx Structure and classification of infinite or finite groups
• 20Fxx Special aspects of infinite or finite groups
• 20Gxx Linear algebraic groups (classical groups) {For arithmetic theory, see 11E57, 11H56; for geometric theory, see 14Lxx, 22Exx; for other methods in representation theory, see 15A30, 22E45, 22E46, 22E47, 22E50, 22E55}
• 20Jxx Connections with homological algebra and category theory
• 20Kxx Abelian groups
• 20L05 Groupoids (i.e. small categories in which all morphisms are isomorphisms) {For sets with a single binary operation, see 20N02; for topological groupoids, see 22A22, 58H05}
• 20Mxx Semigroups
• 20Nxx Other generalizations of groups
• 20P05 Probabilistic methods in group theory [See also 60Bxx]*22-XX Topological groups, Lie groups

#### 22-XX Topological groups, Lie groups

For some useful suggestions see: Lie groups topics

#### 26-XX Real functions

Mean value theorem
for some more suggestions of useful articles to write see also list of mathematical topics

#### 28-XX Measure and integration

• 28Axx Classical measure theory
• 28A05 Classes of sets (Borel fields, $\sigma$-rings, etc.), measurable sets, Suslin sets, analytic sets [See also 03E15, 26A21, 54H05]
• 28A10 Real- or complex-valued set functions
• 28A12 Contents, measures, outer measures, capacities
Lebesgue measure
• 28A15 Abstract differentiation theory, differentiation of set functions [See also 26A24]
• 28A20 Measurable and nonmeasurable functions, sequences of measurable functions, modes of convergence
• 28A25 Integration with respect to measures and other set functions
Lebesgue integral
Bounded convergence theorem
Monotone convergence theorem
Fatou's lemma
• 28A33 Spaces of measures, convergence of measures [See also 46E27, 60Bxx]
• 28A35 Measures and integrals in product spaces
• 28A50 Integration and disintegration of measures
• 28A75 Length, area, volume, other geometric measure theory [See also 26B15, 49Q15]
• 28A78 Hausdorff and packing measures
Hausdorff measure
Hausdorff dimension
Packing dimension
• 28A99 None of the above, but in this section
• 28Bxx Set functions, measures and integrals with values in abstract spaces
• 28Exx Miscellaneous topics in measure theory

#### 31-XX Potential theory

• 31Axx Two-dimensional theory
• 31A05 Harmonic, subharmonic, superharmonic functions
• 31A10 Integral representations, integral operators, integral equations methods
• 31A15 Potentials and capacity, harmonic measure, extremal length [See also 30C85]
• 31A20 Boundary behavior (theorems of Fatou type, etc.)
• 31A25 Boundary value and inverse problems
• 31A30 Biharmonic, polyharmonic functions and equations, Poisson's equation
• 31A35 Connections with differential equations
• 31A99 None of the above, but in this section
• 31Bxx Higher-dimensional theory
• 31B05 Harmonic, subharmonic, superharmonic functions
• 31B10 Integral representations, integral operators, integral equations methods
• 31B15 Potentials and capacities, extremal length
• 31B20 Boundary value and inverse problems
• 31B25 Boundary behavior
• 31B30 Biharmonic and polyharmonic equations and functions
• 31B35 Connections with differential equations
• 31B99 None of the above, but in this section
• 31Cxx Other generalizations
• 31D05 Axiomatic potential theory

#### 33-XX Special functions

(33-XX deals with the properties of functions as functions) {For orthogonal functions, see 42Cxx; for aspects of combinatorics see 05Axx; for number-theoretic aspects see 11-XX; for representation theory see 22Exx}

#### 34-XX Ordinary differential equations

see the current article on differential equations

#### 35-XX Partial differential equations

Schrödinger equation

#### 40-XX Sequences, series, summability

• 40Axx Convergence and divergence of infinite limiting processes
• 40B05 Multiple sequences and series {(should also be assigned at least one other classification number in this section)}
• 40Cxx General summability methods
• 40Dxx Direct theorems on summability
• 40Exx Inversion theorems
• 40F05 Absolute and strong summability
• 40Gxx Special methods of summability
• 40H05 Functional analytic methods in summability

#### 42-XX Fourier analysis

• 42-04 Explicit machine computation and programs (not the theory of computation or programming)
Fourier series
• 42Axx Fourier analysis in one variable
• 42Bxx Fourier analysis in several variables {For automorphic theory, see mainly 11F30}
• 42Cxx Nontrigonometric Fourier analysis

#### 51-XX Geometry

for a list of possible suggestions see list of geometry topics

#### 60-XX Probability theory and stochastic processes

• 60Axx Foundations of probability theory
• 60Bxx Probability theory on algebraic and topological structures
• 60C05 Combinatorial probability
• 60D05 Geometric probability, stochastic geometry, random sets [See also 52A22, 53C65]
• 60Gxx Stochastic processes
• 60Jxx Markov processes
• 60Kxx Special processes

#### 68-XX Computer science

(do we leave it for the computers Workgorup ?)

#### 70-XX Mechanics of particles and systems

(do we leave it for physics Workgroup??)

#### 74-XX Mechanics of deformable solids

(do we leave it for physics Workgroup??)

#### 76-XX Fluid mechanics

(do we leave it for physics Workgroup??)

#### 78-XX Optics, electromagnetic theory

{For quantum optics, see 81V80} (do we leave it for physics Workgroup??)

#### 80-XX Classical thermodynamics, heat transfer

(do we leave it for physics Workgroup??)

#### 82-XX Statistical mechanics, structure of matter

(do we leave it for physics Workgroup??)

#### 85-XX Astronomy and astrophysics

(do we leave it for physics Workgroup??)

#### 86-XX Geophysics

(do we leave it for physics Workgroup??)

#### 91-XX Game theory, economics, social and behavioral sciences

(do we leave it for economy Workgroup??)

#### 92-XX Biology and other natural sciences

(do we leave it for biology Workgroup??)

## References

1. [1]
2. [2]
3. [3]
4. see Planet Math stats page